A sports psychologist performed a study of some visualization techniques that she developed to improve athletic performance. She used amateur golfers and amateur tennis players as participants. In her study,40

%

of the participants were golfers, and the other60

%

were tennis players. (No participant was both a golfer and a tennis player.) The visualization techniques seemed quite helpful for both the golfers and the tennis players:80

%

of the golfers reported a solid improvement in their performance after using the visualization techniques, and70

%

of the tennis players reported a solid improvement in their performance after using the techniques.

Let

G

denote the event that a randomly chosen participant was a golfer andG

denote the event that a randomly chosen participant was a tennis player. LetI

denote the event that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques andI

denote the event that a randomly chosen participant did not report a solid improvement in performance after using the visualization techniques.Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.

(If necessary, consult alist of formulas.)

(a)Fill in the missing probabilities.

P

G

=

0.4

P

G

=

P

I

|

G

=

0.8

P

I

|

G

=

P

I

|

G

=

P

I

|

G

=

0.3

P

G

I

=

P

G

I

=

P

G

I

=

=

P

G

I

(b)What is the probability that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques?